On the Weyl anomaly of Wilson surfaces

TL;DR

This paper calculates the Weyl anomaly for abelian Wilson surfaces using gauge-invariant regularization and explores a Maxwell-like action on a loop space restricted to circular loops.

Contribution

It introduces a gauge-invariant regularization method for computing the Weyl anomaly of Wilson surfaces and derives a Maxwell-type action on a specialized loop space.

Findings

Computed the Weyl anomaly for abelian Wilson surfaces.

Derived a Maxwell-type action on the loop space of circular loops.

Provided insights into gauge-invariant regularization techniques.

Abstract

We compute the Weyl anomaly for an abelian Wilson surface by using a regularization that respects the gauge invariance. We then study the loop space on which lives a one-form connection. We restrict ourselves to the subsector consisting of only circular loops, and derive a Maxwell type action on this restricted loop space.